Inferences on the Coefficients of Variation in a Multivariate Normal Population

In this article, the problem of testing the equality of coefficients of variation in a multivariate normal population is considered, and an asymptotic approach and a generalized p-value approach based on the concepts of generalized test variable are proposed. Monte Carlo simulation studies show that the proposed generalized p-value test has good empirical sizes, and it is better than the asymptotic approach. In addition, the problem of hypothesis testing and confidence interval for the common coefficient variation of a multivariate normal population are considered, and a generalized p-value and a generalized confidence interval are proposed. Using Monte Carlo simulation, we find that the coverage probabilities and expected lengths of this generalized confidence interval are satisfactory, and the empirical sizes of the generalized p-value are close to nominal level. We illustrate our approaches using a real data.     

Randomized nomination sampling for finite populations

We propose a randomized minima–maxima nomination (RMMN) sampling design for use in finite populations. We derive the first- and second-order inclusion probabilities for both with and without replacement variations of the design. The inclusion probabilities for the without replacement variation are derived using a non-homogeneous Markov process. The design is simple to implement and results in simple and easy to calculate estimators and variances. It generalizes maxima nomination sampling for use in finite populations and includes some other sampling designs as special cases. We provide some optimality results and show that, in the context of finite population sampling, maxima nomination sampling is not generally the optimum design to follow. We also show, through numerical examples and a case study, that the proposed design can result in significant improvements in efficiency compared to simple random sampling without replacement designs for a wide choice of population types. Finally, we describe a bootstrap method for choosing values of the design parameters.     

Inference on P(Y < X) in Bivariate Rayleigh Distribution

This paper deals with the estimation of reliability R = P(Y < X) when X is a random strength of a component subjected to a random stress Y, and (X, Y) follows a bivariate Rayleigh distribution. The maximum likelihood estimator of R and its asymptotic distribution are obtained. An asymptotic confidence interval of R is constructed using the asymptotic distribution. Also, two confidence intervals are proposed based on Bootstrap method and a computational approach. Testing of the reliability based on asymptotic distribution of R is discussed. Simulation study to investigate performance of the confidence intervals and tests has been carried out. Also, a numerical example is given to illustrate the proposed approaches.     

Unbiased and almost unbiased ratio estimators of the population mean in ranked set sampling

In this paper we study the problem of reducing the bias of the ratio estimator of the population mean in a ranked set sampling (RSS) design. We first propose a jackknifed RSS-ratio estimator and then introduce a class of almost unbiased RSS-ratio estimators of the population mean. We also present an unbiased RSS-ratio estimator of the mean using the idea of Hartley and Ross (Nature 174:270?C271, 1954) which performs better than its counterpart with simple random sample data. We show that under certain conditions the proposed unbiased and almost unbiased RSS-ratio estimators perform better than the commonly used (biased) RSS-ratio estimator in estimating the population mean in terms of the mean square error. The theoretical results are augmented by a simulation study using a wheat yield data set from the Iranian Ministry of Agriculture to demonstrate the practical benefits of our proposed ratio-type estimators relative to the RSS-ratio estimator in reducing the bias in estimating the average wheat production.     

Testing the equality means of several log-normal distributions

Researches propose various methods for comparing the means of two log-normal distributions. Some of these methods have been recently extended to test the equality means of several log-normal populations. Investigations show that none of the established methods is satisfactory. In this article, we provide three methods based on the computational approach test, which is a parametric bootstrap approach, for testing the means of several log-normal distributions. Further, we compare our methods with the existing methods through Monte Carlo simulation. The numerical results show that the Type I errors of these procedures are satisfactory regardless of the sample size, number of populations, and the true parameters. Finally, we explain the considered methods by real examples.     

An extension of the generalized linear failure rate distribution

In this article, we introduce a new extension of the generalized linear failure rate (GLFR) distributions. It includes some well-known lifetime distributions such as extension of generalized exponential and GLFR distributions as special sub-models. In addition, it can have a constant, decreasing, increasing, upside-down bathtub (unimodal), and bathtub-shaped hazard rate function (hrf) depending on its parameters. We provide some of its statistical properties such as moments, quantiles, skewness, kurtosis, hrf, and reversible hrf. The maximum likelihood estimation of the parameters is also discussed. At the end, a real dataset is given to illustrate the usefulness of this new distribution in analyzing lifetime data.     

Comparing Several Regression Models with Unequal Variances

We consider the problem of comparing k regression models, when the variances are not assumed to be equal. For this problem, the classical F test can lead to misleading results, and there is no simple test which adequately controls the size when the sample sizes are small. For k = 2, the most widely used test is the “weighted F test,” also known as the “asymptotic Chow test.” But this test does not work well for small samples, and various modifications have been proposed in the literature. For k > 2, few tests are available and only the parametric-bootstrap (PB) test of Tian et al. (2009) Tian, L., Ma, C., Vexler, A. (2009). A parametric bootstrap test for comparing heteroscedastic regression models. Communications in Statistics—Simulation and Computation, 38, 1026–1036.[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar] controls the size fairly adequately. In this article, we propose three fairly simple F tests which can easily be applied in the general case, k ? 2, and avoid the complications of the PB test. Our simulations indicate that these tests have satisfactory performance. Also, our simulations confirm that the power properties of our proposed tests are similar to the PB test. Therefore, our proposed tests provide simple alternatives to the PB test, which can easily be used by practitioners who may not be familiar with the PB.     

Posterior Regret Γ-Minimax Estimation and Prediction with Applications on k-Records Data Under Entropy Loss Function

Robust Bayesian analysis is connected with the effect of changing a prior within a class Γ instead of being specified exactly. The multiplicity of prior leads to a collection or a range of Bayes actions. It is interesting not only to investigate the range of estimators but also to recommend the optimal procedures. In this article, we deal with posterior regret Γ-minimax (PRGM) estimation and prediction of an unknown parameter θ and a value of a random variable Y under entropy loss function. Applications for k-records such as estimation and prediction problems are discussed.